Solve Using the Quadratic Formula (x-6)(x+9)=0

$(x - 6) (x + 9) = 0$

Step 1

Simplify the left side.

Simplify $(x - 6) (x + 9)$ .

Expand $(x - 6) (x + 9)$ using the FOIL Method.

Apply the distributive property.

$x (x + 9) - 6 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 - 6 (x + 9) = 0$

Apply the distributive property.

$x \cdot x + x \cdot 9 - 6 x - 6 \cdot 9 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 9 - 6 x - 6 \cdot 9 = 0$

Move $9$ to the left of $x$ .

$x^{2} + 9 \cdot x - 6 x - 6 \cdot 9 = 0$

Multiply $- 6$ by $9$ .

$x^{2} + 9 x - 6 x - 54 = 0$

Subtract $6 x$ from $9 x$ .

$x^{2} + 3 x - 54 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = 3$ , and $c = - 54$ into the quadratic formula and solve for $x$ .

$\frac{- 3 \pm \sqrt{3^{2} - 4 \cdot (1 \cdot - 54)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 54}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 54$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot - 54}}{2 \cdot 1}$

Multiply $- 4$ by $- 54$ .

$x = \frac{- 3 \pm \sqrt{9 + 216}}{2 \cdot 1}$

Add $9$ and $216$ .

$x = \frac{- 3 \pm \sqrt{225}}{2 \cdot 1}$

Rewrite $225$ as $15^{2}$ .

$x = \frac{- 3 \pm \sqrt{15^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{- 3 \pm 15}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 3 \pm 15}{2}$

Step 5

The final answer is the combination of both solutions.

$x = 6, - 9$

Solve Using the Quadratic Formula (x-6)(x+9)=0

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